Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square.
Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points.
[1] To convert between these two formulations of the problem, the square side for unit circles will be L = 2 + 2/dn.
Solutions (not necessarily optimal) have been computed for every N ≤ 10,000.
[2] Dense packings of circles in non-square rectangles have also been the subject of investigations.